Graphene growth on liquid Cu has received great interest, owing to the self-assembly behavior of hexagonal graphene flakes with aligned orientation and to the possibility of forming a single grain of graphene through a commensurate growth of these graphene flakes. Here, we propose and demonstrate a two-step growth process which allows the formation of self-assembled, completely continuous graphene on liquid Cu. After the formation of full coverage on the liquid Cu, grain boundaries were revealed via selective hydrogen etching and the original grain boundaries were clearly resolved. This result indicates that, while the flakes self-assembled with the same orientation, there still remain structural defects, gaps and voids that were not resolved by optical microscopy or scanning electron microscopy. To overcome this limitation, the two-step growth process was employed, consisting of a sequential process of a normal single-layer graphene growth and self-assembly process with a low carbon flux, followed by the final stage of graphene growth at a high degree of supersaturation with a high carbon flux. Continuity of the flakes was verified via hydrogen etching and a NaCl-assisted oxidation process, as well as by measuring the electrical properties of the graphene grown by the two-step process. Two-step growth can provide a continuous graphene layer, but commensurate stitching should be further studied.